Example 1

The geometric mean is the positive square root of the product of the two numbers.

Answer

2

Example 2

What is the geometric mean of 15 and 3?

Hint

Unless you're really good at square roots, you might want to use a calculator for this one.

Answer

6.7

Example 3

What is the length of the altitude of this triangle?

Hint

Make sure your proportion has the altitude on the denominator of the first fraction and the numerator of the second fraction.

Answer

4.7

Example 4

You just bought a 20-foot tall monster TV screen that'll probably burn your retinas before you can finish an episode of Adventure Time. In fact, you have to put it on the floor because otherwise it won't fit in your room. If your eyes are at 5.5 feet and your TV is on the floor, how far away should you stand from the TV so that you can see the whole screen at once?

Hint

You're 5.5 feet tall and the TV is 20 feet tall. That means half the TV is 14.5 feet above your line of sight, and the other half is 5.5 feet below.

Answer

8.93 feet

Example 5

Find the length of x.

Hint

We can use the geometric mean involving the hypotenuses (hypoteni?) and the long sides of the two triangles that involve <em>x</em>.

Answer

9

Example 6

An animatronic bat is being built—because let's face it, who doesn't want an animatronic bat?—with wings in the shape of right triangles. The dimensions are 18 inches for the underside and 15 inches on top. To support its lifelike flight, a beam must be inserted into each wing at the altitude. How long must this beam be, to the nearest tenth of an inch?